Find a function that describes the arithmetic sequence. 15, 30, 45, 60,... Use y to identify each term in the sequence and n to identify each term's position.

Answer:

Step-by-step explanation:

f(g(x)) = \((x-1)^2 = x^2-2x+1\)

The probability of a sample mean of 220 is being greater when the values μ = 210 and α = 35.

μ = 219

σ = 3.5

n = 70

X = 220 (sample mean)

The standard error  can be calculated as:

standard error = σ / \(\sqrt{n}\)

standard error = 3.5 / \(\sqrt{70}\)

standard error = 0.4183

The Z-score will be calculated by using the formula:

z = (X - μ) / SE

z = (220 - 219) / 0.4183

z = 2.3881

The value of Z at  2.3881 is 0.87% by using the standard normal distribution table.

Now let us calculate the second part where μ = 210 and α = 35.

μ = 210

σ = 35

n = 70

X = 220 (sample mean)

The standard error can be calculated as:

SE = σ / \(\sqrt{n}\)

SE = 35 /  \(\sqrt{70}\)

SE = 4.1833

Now, the z score will be calculated as:

z = (X - μ) / SE

z = (220 - 210) / 4.1833

z = 2.3894

The value of Z at 2.3894 is  0.86% by using the standard normal distribution table.

Therefore we can conclude that the probability of a sample mean of 220 is greater when μ = 210 and α = 35.

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The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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x = 2 to x = 5 is 4.

To find the average rate of change of a function, you need to subtract the initial value from the final value and divide it by the change in the input variable. Here's how to use a calculator to find the average rate of change of a function:Step 1: Input the initial value of the input variable into the calculator.Step 2: Input the final value of the input variable into the calculator.Step 3: Subtract the initial value from the final value.Step 4: Divide the difference by the change in the input variable. Example:Find the average rate of change of the function f(x) = 3x - 1 from x = 2 to x = 5.Step 1: Input 2 into the calculator.Step 2: Input 5 into the calculator.Step 3: Subtract 3(2) - 1 from 3(5) - 1. The result is 14.Step 4: Divide 14 by 5 - 2. The result is 4.Therefore, the average rate of change of f(x) from x = 2 to x = 5 is 4.

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Step-by-step explanation:

Knowing that f(x) = 2x^2 - x - 4 and f^2(x) means f(f(x)), we get:

f^2(x) = f(f(x)) = 2(2x^2 - x - 4)^2 - (2x^2 - x - 4) - 4.....

You have to square the whole thing... You'll get a 4th degree equation. I know it's a bit boring .... but whatever.

Answer:

a] is 8cm

Step-by-step explanation:

A=2a2+4ah

a=8cm

h=15cm

therefore A=608

a. Length of each side of the square base = 8 cm

b. Surface area of the candle = surface area of square prism = 608 cm²

Surface area of square prism = 2a² + 4ah, where a is the length of each side of the square base, and h is the height of the prism.

Volume = a²h.

Given the following:

a. Volume = a²h

Substitute

960 = (a²)(15)

960/15 = a²

64 = a²

a = √64

a = 8 cm

Therefore, the length of each side of the square base = 8 cm.

b. Surface area of the candle = surface area of square prism = 2a² + 4ah = 2(8²) + 4(8)(15)

Surface area of the candle = 608 cm²

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Answer:

4/8 or reduced 1/2

Step-by-step explanation:

It's 4/8 or reduced as 1/2 because there are 4 even numbers 2, 4, 6, 8

Answer:

A,B,D,E

Step-by-step explanation:

The statements which are true shown below,

From graph attached below, It is observed that

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Answer:

x = 2.7

Step-by-step explanation:

5.4 = 2x

2x = 5.4

Divide both sides by 2.

x = 2.7

Answer: x= 2.7

1. Divide 2 on both sides

2. cancel terms who have the same numerator and denominator

Answer:

they arrive at the same time

Step-by-step explanation:

the triangle is like the Pythagorean theorm

both the purple lines equal a^2+b^2

and the green line equals c^2

a^2+b^2=c^2

Answer:

A (-2, 10)

Step-by-step explanation:

If you plug in the point into x and y you should get "false" on a calculator, or the answer won't make sense, meaning that it's not a part of the set

(-2,10) is not the solution set of the given equation \(3y+2 =x^{2} -5x+17\).

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

According to the given question

We have an equation

\(3y + 2 =x^{2} -5x+17\)

The above equation can be written as

\(x^{2} -5x +17-3y-2=0...(i)\)

For finding the point which is not the solution set of the equation, first we will substitute the given points in the above equation and check whether it making the equation true or not.

For point (-2, 10)

Substitute, x = -2 and y = 10 in the equation (i)

\((-2)^{2} -5(-2) + 17 - 3(10) -2\\=4+10+17-30-2\\= -1\neq 0\)

Hence, (-2, 10) is not the solution of the given equation.

For point (5, 5)

Substitute, x = 5, and y = 5 in equation (i)

\((5)^{2} -5(5)+17-3(5)-2\\=25-25+17-15-2\\=0\)

Hence, (5, 5) is the solution of the given equation.

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Answer:

Undefined

Step-by-step explanation:

-4-1/-6+6

Since the bottom adds up to zero and you cannot simplify a fraction with 0 as the denominator, the slope is undefined.

Answer:

Undefined

Step-by-step explanation:

Hi student! Let me help you out on this question.

_________________

- - - - - - - - - - - - - - - - - - - -

We can find the slope, using the formula.

\(\mathrm{\cfrac{y2-y1}{x2-x1}}\).

Plugin the values.

\(\mathrm{\cfrac{-4-1}{-6-(-6)}}\)

                                  ↪

Do you see what I see?

 To find out, simplify further.

\(\mathrm{\cfrac{-3}{-6+6}}\). Simplifying completely results in.

\(\mathrm{\cfrac{-3}{0}}\).

We know that we cannot divide by zero.

\(\therefore\mathrm{Slope=unde fined}}\). Which is our answer.

Hope that this helped you out! have a good day ahead.

Best Wishes!

\(\star\bigstar\textsf{Reach far. Aim high. Dream big.}\bigstar\star\).

◈◈-Greetings!-◆◆

- - - - - - - - - - - - - - - - - -

______________________

Answer:

Congruent angles

Step-by-step explanation:

The 2 angles are Corresponding angles and are congruent

32% of the same people spend their time listening.

The total number of mentioned  people will be 100% or 1. Now, in the total people, the remaining ones who are not stated in the question, must be the listeners. Thus, calculating the remaining percentage of people, we will get the percentage of listeners in same people.

So, number of people who spend time speaking = 26%

Number of people who spend time speaking = \(\frac{26}{100}\)

Number of people who spend time speaking = 0.26

Number of people who spend time writing =  23%

Number of people who spend time writing = \(\frac{23}{100}\)

Number of people who spend time writing = 0.23

Number of people who spend time reading =  19%

Number of people who spend time reading = \(\frac{19}{100}\)

Number of people who spend time reading = 0.19

Total number of people involved in activities other than listening = 0.26 + 0.23 + 0.19

Total number of people involved in activities other than listening = 0.68

People who spend time listening = 1 - 0.68

People who spend time listening = 0.32

Percentage of people who spend time listening = 0.32 × 100

Percentage of people who spend time listening = 32%

Hence, 32% of the same people spend their time listening.

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Answer:

Discriminant is -20 (D<0, no real roots)

Step-by-step explanation:

The Discriminant Formula:

\( \displaystyle \large{ D = {b}^{2} - 4ac}\)

First, arrange expression in the standard form or ax^2+bx+c = 0.

\( \displaystyle \large{ {x}^{2} - 4x = 9} \\ \displaystyle \large{ {x}^{2} - 4x - 9 = 0}\)

From above, we subtract both sides by 9.

Compare the coefficients:

\( \displaystyle \large{a {x}^{2} + bx + c = {x}^{2} - 4x - 9}\)

Substitute a = 1, b = -4 and c = -9 in the formula.

\( \displaystyle \large{ D = {( - 4)}^{2} - 4(1)( - 9)} \\ \displaystyle \large{ D = 16 - 4( - 9)} \\ \displaystyle \large{ D = 16 - 36} \\ \displaystyle \large{ D = - 20}\)

Therefore the discriminant of equation is -20 which is less than 0.

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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The z-score for a subject with a score of 34 on this standardized test is approximately -2.37. This indicates that the subject's score is about 2.37 standard deviations below the population mean. The negative sign indicates that the score is below the mean.

The z-score for a subject who earns a score of 34 on a standardized test with a population mean of 115 and a standard deviation of 30 is approximately -2.37.

The z-score measures the number of standard deviations a raw score is from the mean of a distribution. It is calculated using the formula:

z = (x - μ) / σ

Where:

z is the z-score,

x is the raw score,

μ is the population mean, and

σ is the population standard deviation.

In this case, the subject's raw score is 34, the population mean is 115, and the standard deviation is 30. Plugging in these values into the formula, we have:

z = (34 - 115) / 30 ≈ -2.37

Therefore, the z-score for a subject with a score of 34 on this standardized test is approximately -2.37. This indicates that the subject's score is about 2.37 standard deviations below the population mean. The negative sign indicates that the score is below the mean.

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Answer:

the answer is 5.0 x 10 to the -4th power mm

Step-by-step explanation:

i just guessed and i got it right on my quiz

Answer:

It is C.

Step-by-step explanation:

Answer:

The method for appearing with numbers for the 2x2 matrix whose determinant is 13 is clarified.

Step-by-step explanation:

Determinant of 2×2 matrix

If we have a 2×2 matrix A of the form;

A =

\binom{a \: \: \: b}{c \: \: \: d}(

cd

ab

)

The determinant of the matrix is;

|A| = (a.d) - (b.c)

Therefore, to appear with numbers for a, b, c, and d, we must ensure; (a.d) - (b.cdeterminantse, if a = 3, d = 15, b = 2, and v = 1.

Ultimately, |A| = (3×5) - (2×1) = 13

Therefore, Chase ran 49/8 miles each day.

To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).

First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.

Now, we can divide 147/4 by 6 to find the distance he ran each day:

(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.

Therefore, Chase ran 147/24 miles each day.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.

So, dividing 147 and 24 by 3, we get:

147/3 / 24/3 = 49/8.

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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.

To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.

Now, we can divide the total distance by the total number of days:

36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.

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Answer: $2,466.45

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:

A = P (1 + r/n) nt

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r =  Nominal Interest Rate (decimal form, 3.5/100= 0.035)

n=   number of compounding periods in each year (365)

Replacing with the values given

3,500= P (1+ 0.035/365)^365(10)

Solving for P

3,500= P (1.00009589)^3650

3,500/  (1.00009589)^3650 =P

P = $2,466.45

The area A of the region S that lies under the graph of the continuous function f is \(\frac{1}{4}\).

(a)

\(A =\)  \(\int\limits^A_b {f(x)} \, dx\)  

   = \(\lim_{n \to \infty}\)∑ f(xi) Δ x

a = 0, b = 1 → Δ x = \(\frac{1-0}{n}\) = \(\frac{1}{n}\)

x₀ = 0, x₁ = \(\frac{1}{n}\) , x₂ = \(\frac{2}{n}\), x₃ = \(\frac{3}{n}\), ..., xi = \(\frac{i}{n}\)

f(x) = \(x^{3}\)

f(xi) = \([\frac{i}{n} ]^{3}\) = \(\frac{i^{3} }{n^{3} }\)

Then,

A = \(\lim_{n \to \infty}\) ∑(\(\frac{i^{3} }{n^{3} }\)) * \(\frac{1}{n}\)

(b)

A = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * ∑ \(\frac{i^{3} }{n^{3} }\) ]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * \(\frac{1}{n^{3} }\) ∑ \(i^{3}\)]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * [\(\frac{n(n+1)}{2}\)]^2]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * \(\frac{n^{2}(n+1)^{2} }{4}\)]  

  = \(\lim_{n \to \infty}\) \(\frac{(n+1)^{2} }{4n^{2} }\)

  = \(\frac{1}{4}\) * \(\lim_{n \to \infty}\) \((\frac{n+1}{n} )^{2}\)

  = \(\frac{1}{4}\) * \(1^{2}\)

A = \(\frac{1}{4}\)

Therefore the area A of the region is \(\frac{1}{4}\).

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The resulting function is f(x) = (5/5)x^5 + (4/4)x^4 + (4/2)x^2 + 7x - 15. To find f(x), we need to integrate f "(x) with respect to x. We know that the derivative of a function is the rate of change of that function with respect to its independent variable.

So, integrating the second derivative of a function will give us the function itself.

Therefore, integrating f "(x) = 20x^3 + 12x^2 + 4 with respect to x, we get f'(x) = 5x^4 + 4x^3 + 4x + C1, where C1 is a constant of integration.

Now, using the given information that f(0) = 7, we can find the value of C1.

f(0) = 7
f'(0) = 0 + 0 + 0 + C1 = 0 + C1 = 7
C1 = 7

Thus, f'(x) = 5x^4 + 4x^3 + 4x + 7

Integrating f'(x) with respect to x, we get f(x) = (5/5)x^5 + (4/4)x^4 + (4/2)x^2 + 7x + C2, where C2 is another constant of integration.

Using the given information that f(1) = 3, we can find the value of C2.

f(1) = (5/5)1^5 + (4/4)1^4 + (4/2)1^2 + 7(1) + C2 = 5 + 4 + 2 + 7 + C2 = 18 + C2 = 3
C2 = -15

Therefore, the function f(x) is:

f(x) = (5/5)x^5 + (4/4)x^4 + (4/2)x^2 + 7x - 15

In summary, the function f(x) can be found by integrating the second derivative of f(x) given in the question. The constants of integration are then found using the given information about the function's values at certain points. The resulting function is f(x) = (5/5)x^5 + (4/4)x^4 + (4/2)x^2 + 7x - 15.

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Answer:

Two

Step-by-step explanation:

hope this helps tell me if I'm wrong though

Answer:

the new side lengths are 10.5 , 9 and 6 inches

the new triangle has the following sides: 5, 4, 3 inches

the perimeter of the first triangle is 36 inches

the perimeter of the second triangle is 12 inches

area of the first triangle is 54 inches squared

area of the second triangle is 6 inches squared

Step-by-step explanation:

first question:

sides are 7,6,4. multiply each one by 3/2 or 1.5

7 x 1.5 = 10.5 or 12/2

6 x 1.5 = 9

4 x 1.5 = 6

the new side lengths are 10.5 , 9 and 6 inches

second question:

multiply each side by 1/3

the sides are 15, 12, 9, so:

15 x 1/3= 5

12 x 1/3 = 4

9 x 1/3 = 3

the new triangle has the following sides: 5, 4, 3

normal sides are 3 and 4

hypotenuse is 5

question a: (calculate perimeter)

the perimeter of a triangle: you add all the sides

the first triangle has 15, 12, 9 for its sides so:

15+12+9 = 36

the perimeter of the first triangle is 36

the second triangle has 5,4,3 for its sides so:

5+4+3 = 12

the perimeter of the second triangle is 12

question b: (calculate the area of both triangles)

area of a triangle: h x b/2: height times base divided by 2

the first triangle has sides, 15,12,9

height is 9 and base is 12, so:

9 x 12/2 = 54 inches squared

area of the first triangle is 54 inches squared

the second triangle has sides, 5,4,3

height is 3 and base is 4, so:

3 x 4/2 = 6 inches squared

area of the second triangle is 6 inches squared

If we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units.

Assuming you meant to say "let f be a differentiable function where f(9) = 4 and f'(9) = 3. If we change x by -0.7 and we change y by 0.3, then we can expect the value of f(x) to change by approximately what amount?"

Using the linear approximation formula, we have:

\(Δf(x) ≈ f'(9) Δx\)

where Δx = -0.7 and we want to find Δf(x) when Δy = 0.3.

We can rearrange the formula to solve for Δf(x):

\(Δf(x) ≈ f'(9) Δx\)

Δf(x) ≈ 3(-0.7)

Δf(x) ≈ -2.1

This means that if we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units. However, this is only an approximation based on the linear behavior of the function near x = 9, so it may not be exactly accurate for large changes in x.

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The phase of inferential statistics which is sometimes considered to be the most crucial because errors in this phase are the most difficult to correct is "data gathering".

Inferential statistics are frequently employed to compare treatment group differences.

Some characteristics of inferential statistics are-

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Check the picture below.